{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:74Q7FZY6THP6TYZOYGVPU6B4CE","short_pith_number":"pith:74Q7FZY6","schema_version":"1.0","canonical_sha256":"ff21f2e71e99dfe9e32ec1aafa783c110337374f376c8baed68f1e451bb7c607","source":{"kind":"arxiv","id":"1709.05846","version":1},"attestation_state":"computed","paper":{"title":"Hypermonogenic solutions and plane waves of the Dirac operator in Rp x Rq","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Al\\'i Guzm\\'an Ad\\'an, Franciscus Sommen, Heikki Orelma","submitted_at":"2017-09-18T10:23:02Z","abstract_excerpt":"In this paper we first define hypermonogenic solutions of the Dirac operator in Rp x Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.05846","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-18T10:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"909bc500588a6862230c57c9770b031bf9e8b2792187828100d3a4e34c331426","abstract_canon_sha256":"8088fca954e217b438c9433214883f4d96a0410a4a2d962bca2a5df0c248f31e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:59.151783Z","signature_b64":"odJLnaj2KldE+mzKK1WVpbI+H1iWueOB0mzxx5BaE6jxfaW4VaZsVrC6t3I/4MMboT+e+mo1c7aN/+MEWgsUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff21f2e71e99dfe9e32ec1aafa783c110337374f376c8baed68f1e451bb7c607","last_reissued_at":"2026-05-18T00:34:59.151048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:59.151048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypermonogenic solutions and plane waves of the Dirac operator in Rp x Rq","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Al\\'i Guzm\\'an Ad\\'an, Franciscus Sommen, Heikki Orelma","submitted_at":"2017-09-18T10:23:02Z","abstract_excerpt":"In this paper we first define hypermonogenic solutions of the Dirac operator in Rp x Rq and study some basic properties, e.g., obtaining a Cauchy integral formula in the unit hemisphere. Hypermonogenic solutions form a natural function class in classical Clifford analysis. After that, we define the corresponding hypermonogenic plane wave solutions and deduce explicit methods to compute these functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05846","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.05846","created_at":"2026-05-18T00:34:59.151165+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.05846v1","created_at":"2026-05-18T00:34:59.151165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05846","created_at":"2026-05-18T00:34:59.151165+00:00"},{"alias_kind":"pith_short_12","alias_value":"74Q7FZY6THP6","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"74Q7FZY6THP6TYZO","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"74Q7FZY6","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE","json":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE.json","graph_json":"https://pith.science/api/pith-number/74Q7FZY6THP6TYZOYGVPU6B4CE/graph.json","events_json":"https://pith.science/api/pith-number/74Q7FZY6THP6TYZOYGVPU6B4CE/events.json","paper":"https://pith.science/paper/74Q7FZY6"},"agent_actions":{"view_html":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE","download_json":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE.json","view_paper":"https://pith.science/paper/74Q7FZY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.05846&json=true","fetch_graph":"https://pith.science/api/pith-number/74Q7FZY6THP6TYZOYGVPU6B4CE/graph.json","fetch_events":"https://pith.science/api/pith-number/74Q7FZY6THP6TYZOYGVPU6B4CE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE/action/storage_attestation","attest_author":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE/action/author_attestation","sign_citation":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE/action/citation_signature","submit_replication":"https://pith.science/pith/74Q7FZY6THP6TYZOYGVPU6B4CE/action/replication_record"}},"created_at":"2026-05-18T00:34:59.151165+00:00","updated_at":"2026-05-18T00:34:59.151165+00:00"}